The invention relates to a multi-node immittance network producing between the input nodes an immittance with a real component proportional to the square of the frequency.
Networks of this type were first disclosed by L. T. Bruton, e.g. Proceedings of the IEEE, August 1968, pages 1378/9, "Frequency Selectivity Using Positive Impedance Converter-type Networks" and IEEE Transactions on Circuit Theory, August 1969, pages 406 to 408, "Network Transfer Functions Using The Concept Of Frequency-Dependent Negative Resistance". More particularly, such networks can produce a real negative admittance proportional to the square of the frequency and such elements may have various applications, e.g. in filters, oscillators, etc., since they represent yet another way to avoid physical inductances in the realization of various immittance networks.
In telecommunication filters, for instance, it was previously known to replace physical inductances in a filter design by active circuits simulating the latter and, more particularly, a capacitively loaded gyrator which is equivalent to an inductance. However, when the filter inductances are in a series branch or more generally are floating elements with no grounded terminal, the realization using gyrators, for instance, is awkward and relatively costly since an ungrounded inductor must be simulated by two gyrators and with current operational amplifier solutions. In this solution each of the gyrators need two operational amplifiers making a total of four operational amplifiers for the simulated ungrounded inductance.
With Bruton filters, however, starting from a conventional LCR filter design, an impedance transformation is used in such a way that multiplying all the elements by a common scaling factor inversely proportional to the frequency, all resistances become capacitances, all inductances are transformed into resistances and finally all capacitances become FDNR (Frequency-Dependent Negative Resistances) elements of Bruton or so-called supercapacitances, i.e. negative conductances proportional to the square of the frequency. Such supercapacitances can be realized, like gyrators and other similar impedance converters or inverters, by using operational amplifiers and in a low-pass filter using original grounded capacitances only, the Bruton concept is particularly attractive since these will be replaced by grounded super capacitances which need only two operational amplifiers, all the remaining elements of the transformed filter being resistances and capacitances, the latter corresponding to the original source and load resistances for the filter.
Nevertheless, two operational amplifiers are still needed per supercapacitance, even when the latter is grounded, and a general object of the present invention is to reduce this to a single operational amplifier.